### Introduction

Have you ever noticed that when a train or car moves past you rapidly its whistle or horn seems to change to a lower note? In 1842 an Austrian Physicist, Hans Christian Doppler, asserted that sound waves emitted by a moving train would have a higher frequency when moving toward a listener and a lower frequency when moving away. For surface waves in water, Doppler predicted the same type of frequency shift. In particular, a decrease in the frequency of waves propagating behind a source that moves away at a speed vs can be predicted using the Doppler equation

${f_{\text{B}}} = {f_0}\frac{{{v_{\text{w}}}}} {{{v_{\text{w}}} + {v_{\text{s}}}}}$

where vw is the speed of wave propagation in water and f0 is the frequency of the waves created by a stationary source. Doppler also predicted that the frequency increase in front of a source is given by

${f_{\text{F}}} = {f_0}\frac{{{v_{\text{w}}}}} {{{v_{\text{w}}} - {v_{\text{s}}}}}$

### Objectives

In this activity, you will

• Verify the Doppler Equations for surface waves in water by using Logger Pro to analyze two high speed movies.